A computer program listing appendix has been submitted on two, identical compact discs in computer readable form, labeled xe2x80x9cCopy 1xe2x80x9d and xe2x80x9cCopy 2xe2x80x9d, which is a duplicate of xe2x80x9cCopy 1xe2x80x9d disc. The material contained in this computer program listing appendix is herein incorporated by reference.
As a demonstration of a working implementation of the complete multivariate data analysis method, according to an embodiment of the present invention, the following software executable routines were implemented in MATLAB(copyright) language, MathWorks, Inc., Natick, Mass., and stored on a computer readable medium. Intel Math Kernel Library (MKL) and LAPACK routines (www.netlib.org) were incorporated as xe2x80x9cmex-filesxe2x80x9d. The source code, which is supplied as a Computer Program Listing Appendix on Compact Disk, and herein is incorporated by reference, includes the following files listed in Table 1.
The present invention relates generally to the field of chemical compositional analysis, and more specifically to a method and apparatus for performing multivariate spectral analysis.
In general, multivariate spectral analysis for chemical microanalytical characterization of a sample can include: (1) determining the number of chemical species (pure elements and chemical phases or alloys) that comprise the inhomogeneous mixture being imaged; (2) extracting the spectra of these xe2x80x9cpurexe2x80x9d components (elements or phases); (3) quantifying the amount or concentration of each component present in the sample; and (4) mapping the spatial distribution of these components across the sample, while simultaneously preserving a high spatial resolution. Full spectrum images refer to a complete spectrum that is produced at each pixel of 2-D array of pixels (i.e., image).
Spectral data can be produced by a variety of microanalytical techniques, including: Electron Probe Microanalysis (EPMA), also called X-Ray Microanalysis (XMA) in Japan, Scanning Electron Microscopy (SEM) with attached Energy Dispersive Spectrometer (EDS), X-ray fluorescence (XRF), Electron Energy Loss spectroscopy (EELS), Particle Induced X-ray Emission (PIXE), Auger Electron Spectroscopy (AES), gamma-ray spectroscopy, Secondary Ion Mass Spectroscopy (SIMS), X-Ray Photoelectron Spectroscopy (XPS), Raman Spectroscopy, Magnetic Resonance Imaging (MRI) scans, Computerized Axial Tomography (CAT) scans, IR reflectometry, etc.
The spectral data can be generated from a spot on the sample, from a 1-D line scan, or from a 2-D rastered pattern. Other dimensions, however, can be time or temperature, for example. Hence, the spectral data can vary with time, for example, as a chemical reaction process evolves over time, or from species diffusing across an interface, or concentrations that vary with temperature as the sample heats up.
A spectrum is created by detecting radiation (e.g., photons or particles) emitted within a specified interval (window) of energy (mass, wavelength, or frequency), as a function of energy (mass, wavelength, or frequency). In other words, we measure the energy (or mass, wavelength, or frequency) of emitted photons (or particles) and then xe2x80x9cbinxe2x80x9d them according to their energy (mass, wavelength, or frequency). The spectrum is basically a histogram that results from this binning process. The spectrum generally includes well-defined spectral features that have a characteristic energy distribution (mass, wavelength, or frequency).
We define xe2x80x9cspectral featuresxe2x80x9d to include sharp, well-defined spectral peaks, as well as double-peaks, overlapping peaks, and less well-defined maxima.
The phrase xe2x80x9cenergy spectrumxe2x80x9d is broadly defined to also include a xe2x80x9cmass spectrumxe2x80x9d (for mass spectroscopy), a xe2x80x9cwavelength spectrumxe2x80x9d (for wavelength dispersive analysis, WDS), a xe2x80x9cfrequency spectrumxe2x80x9d (for Fast Fourier Transform analysis), or an xe2x80x9cacoustic spectrumxe2x80x9d (for sound/speech analysis).
The word xe2x80x9ccharacteristicxe2x80x9d broadly relates to a property that is typical or characteristic of a material""s unique individual atomic or molecular structure. For example, in X-ray spectroscopy, xe2x80x9ccharacteristicxe2x80x9d refers to a specific electronic transition in the element""s atomic structure resulting in emission of an X-ray having a well-known energy. However, in infrared spectroscopy, the characteristic property relates to vibrational transitions; and in mass spectroscopy, to the mass of fragments. Additionally, the spectrum can includes contributions from non-xe2x80x9ccharacteristicxe2x80x9d sources (e.g., continuum radiation from background or Bremsstrahlung X-radiation), which are continuous and don""t have characteristic peaks or lines. Inspection of the detected spectrum allows the chemical composition to be determined by comparison of the spectral peaks with spectra measured from known elements or phases, which can found in lookup tables in data libraries, books, etc.
In electron probe microanalysis (EPMA), for example, a pre-selected small area on the surface of a solid specimen is bombarded with energetic electrons (e.g., 20 KeV electrons). The resulting emission from the sample includes a variety of particles and photons, including: backscattered primary electrons, low-energy photoelectrons, Auger electrons, and characteristic X-ray emission superimposed on a background of continuum (i.e., Bremsstrahlung) X-radiation. The X-rays emitted by the sample are counted and recorded by an X-ray detector, a crystal spectrometer, or an Energy Dispersive Spectrometer (EDS). A multi-channel EDS spectrum analyzer (e.g., with 1024 xe2x80x9cenergyxe2x80x9d channels) is used to count the number of X-rays randomly emitted during the counting period within a single channel (i.e., a small band of energy having a width, xcex94E. For example, xcex94E can be equal to 10 eV. A 2-D xe2x80x9cfull spectrumxe2x80x9d image is generated by scanning and rastering a focused electron beam spot across the surface of a sample, at a specified spatial resolution (e.g., 128xc3x97128 pixels). For each pixel, a multi-channel (e.g., 1024) X-ray spectrum is detected by the EDS. A full spectrum image contains, for example, a 3-D array of 128xc3x97128xc3x971024=16.8 million data points. The measured X-ray spectrum from a single pixel can have spectral contributions integrated from not only multiple elements, but also multiple phases.
The word xe2x80x9csamplexe2x80x9d is not limited to representing a small, conventional specimen that would be used, for example, in a Scanning Electron Microscope. xe2x80x9cSamplexe2x80x9d is broadly defined to mean any surface area or volume of a material that is emitting radiation that can be detected by a detector. For example, the word xe2x80x9csamplexe2x80x9d can include the Earth""s (or Moon""s) surface, which may be emitting radiation (in response to irradiation by Sunlight) that can be detected by an array of CCD detectors located on a satellite in orbit around the Earth (or Moon). The xe2x80x9csamplexe2x80x9d can also include astronomical objects, such as stars and galaxies, which emit radiation detected by telescopes.
The phrase xe2x80x9cradiation emitted by the samplexe2x80x9d is broadly defined to include any type of photon or particle, including, but not limited to: radio waves, microwaves, visible light, infrared radiation, ultraviolet radiation, X-rays, gamma-rays, electrons, positrons, protons, neutrons, neutral particles, alpha particles, charged particles (ions), ionized atoms, ionized molecules, excited molecules. We also include in this broad definition of xe2x80x9cradiation emitted by the samplexe2x80x9d the emission of acoustic energy (i.e., sound waves). We also include in this broad definition of xe2x80x9cradiation emitted by the samplexe2x80x9d the transmission of radiation through a sample, either completely or partially, which is subsequently xe2x80x9cemittedxe2x80x9d from the far side of the sample. Emission is defined to include the scattering or reflection of particles from a surface. Particles may be xe2x80x9cemittedxe2x80x9d from a sample by sputtering processes (as in SIMS).
Emission of radiation from the sample can result from stimulation of the sample by an external source, or from naturally radioactive elements (isotopes) contained within. Emitted xe2x80x9cradioactivexe2x80x9d particles can include beta (electrons), gammas (high-energy photons), alpha particles (helium ions), neutrons, and other particles. Emitted radioactive particles can interact with the surrounding material in the sample and induce or stimulate other forms of radiation to be emitted in response to the flux of radioactive particles.
The phase xe2x80x9csimulating a sample to emit radiationxe2x80x9d is defined as applying an external stimulus that can include exposing (irradiating) the sample to: radio waves, microwaves, visible light, infrared radiation, ultraviolet radiation, X-rays, gamma-rays, electrons, positrons, protons, neutrons, neutral particles, alpha particles, or charged particles (ions). Additionally, applying an external stimulus can include passing an electric current through the sample, inducing ultrasonic vibrations, or mechanically stressing the sample (e.g., pulling or bending the sample to create acoustic emission). Application of the external radiation can include irradiation by a single probe beam, or parallel irradiation by a plurality of multiple, parallel beams.
Against this background, the present invention was developed.